Dynamic Programming or DP

Dynamic Programming is an algorithmic technique with the following properties.

• It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming.
• The idea is to simply store the results of subproblems so that we do not have to re-compute them when needed later. This simple optimization typically reduces time complexities from exponential to polynomial.
• Some popular problems solved using Dynamic Programming are Fibonacci Numbers, Diff Utility (Longest Common Subsequence), Bellman–Ford Shortest Path, Floyd Warshall, Edit Distance and Matrix Chain Multiplication.

Basic of DP

• Introduction to DP
• Tabulation vs Memoization
• Steps to solve a DP Problem

Basic Problems

• Fibonacci numbers
• Tribonacci Numbers
• Lucas Numbers
• Climbing Stairs
• Climbing Stairs with 3 Moves
• Weighted Climbing Stairs
• Maximum Segments
• nth Catalan Number
• Count Unique BSTs
• Count Valid Parenthesis
• Ways to Triangulate a Polygon
• Min Sum in a Triangle
• Minimum Perfect Squares
• Ways to Partition a Set
• Binomial Coefficient
• Pascal's Triangle
• Nth Row of Pascal Triangle
• Min Sum in a Triangle

Easy Problems

• House Robber
• Min Cost Path
• Decode Ways
• Subset Sum Problem
• Coin change problem - Count Ways
• Coin Change – Minimum Coins to Make Sum
• Painting Fence Algorithm
• Cutting a Rod
• Jump Game
• Longest Common Substring
• Count all paths in a Grid
• Paths in a Grid with Obstacles
• Permutations with K Inversions
• Max A's using Special Keyboard

Medium Problems

• Water Overflow
• Longest Common Subsequence
• Longest Increasing Subsequence
• Edit Distance
• Largest Divisible Subset
• Weighted Job Schedulling
• 0-1 Knapsack Problem
• Printing Items in 0/1 Knapsack
• Unbounded Knapsack
• Word Break Problem
• Tile Stacking Problem
• Box-Stacking Problem
• Partition Problem
• Longest Palindromic Subsequence
• Longest Common Increasing Subsequence (LCS + LIS)
• All distinct subset (or subsequence) sums
• Count Derangements
• Minimum insertions for palindrome
• Wildcard Pattern Matching
• Regular Expression Matching
• Arrange Balls with adjacent of different types
• Longest Subsequence with 1 adjacent difference
• Maximum size square sub-matrix with all 1s
• Bellman–Ford Algorithm
• Floyd Warshall Algorithm
• Maximum Tip Calculator

Hard Problems

• Largest X Bordered Square
• Egg Dropping Problem
• Palindrome Partitioning
• Palindromic Substring Count
• Word Wrap Problem
• Optimal Strategy for a Game
• The painter’s partition problem
• Program for Bridge and Torch problem
• Matrix Chain Multiplication
• Printing Matrix Chain Multiplication
• Maximum sum rectangle
• Stock Buy and Sell - At-Most k Times
• Stock Buy and Sell - At Most 2 Times
• Min cost to sort strings using Reversals
• Count of AP Subsequences
• DP on Trees
• Max Height of Tree when any Node can be Root
• Longest repeating and non-overlapping substring
• Palindrome Substrings Count

DP Problems Sorted by Topic / Dimensions / Standard Problems

• DP Standard Problems and Variations.
• DP Problems Dimension Wise (1D, 2D and 3D)
• DP Problems Topic Wise

Advanced Concepts in Dynamic Programming (DP)

• Bitmasking and Dynamic Programming | Set 1
• Bitmasking and Dynamic Programming | Set-2 (TSP)
• Digit DP | Introduction
• Sum over Subsets | Dynamic Programming

Quick Links:

• Learn Data Structure and Algorithms | DSA Tutorial
• Top 20 Dynamic Programming Interview Questions
• ‘Practice Problems’ on Dynamic Programming
• ‘Quiz’ on Dynamic Programming

Introduction to DP

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Introduction to DP

Dynamic Programming - Memoization

Dynamic Programming - Tabulation